Using Roman names
This article contains general guidance on how to use Roman names. It must be stressed that these are not firm legalistic rules. A name is a device which allows one person to talk about another person so that everyone knows who he is talking about. Any rule which makes it unclear who is being referred to would be self-defeating, and all the general rules explained below should be ignored if following them would lead to confusion.
Usage of the Roman names
How Many Names?
As a general rule, the more formal the context, the more names are used. The use of all three (or more) names is very formal, and should be rare. Calling someone M. Tullius Cicero is roughly equivalent to calling someone Mr Robert James Grant, Esquire.
Two names are normally enough to make it clear who you are talking to or about. Using two names is formal and polite. Calling someone M. Tullius is roughly equivalent to calling someone Robert Grant or Mr Grant. When you mention someone for the first time in a speech or a letter, or when greeting someone, it is common to use two names.
Use of one name is relatively relaxed and informal. If you already in the middle of a conversation with someone, or in the middle of talking about someone, you might well call him by just one name, especially if you know him reasonably well. Calling someone Cicero is roughly equivalent to calling someone Robert. But in formal situations or when first mentioning someone, using only one name may be over-familiar and could be impolite.
Which names you call someone by depends partly on how many names you are using.
When calling someone by two names, which names you use depends on the status of the person you're naming. If the person is a nobilis, it is proper to call him by his praenomen and cognomen, e.g. P. Scipio. If he is a homo novus, one would normally call him by his praenomen and nomen, e.g. M. Tullius. Most people in Nova Roma are homines novi, so most people are normally called by their praenomen and nomen. If you accidentally call a nobilis as if he were a homo novus, he will probably not take offence, especially if you apologize for your mistake; but if in doubt, you can always ask.
One may, of course, flatter or praise a novus homo by naming him with his praenomen and cognomen as if he were a nobilis; but you should not do this too often, especially as it could cause resentment among the true nobiles.
Some people adopt a style which was fashionable in the first generations of the imperial period and call everyone, both nobilis and homo novus, by nomen and cognomen, e.g. Cornelius Scipio, Tullius Cicero. There is nothing strictly wrong with this, but it is not characteristic of the ancient republic and is not encouraged.
When calling someone by only one name, it is normal to use the nomen or cognomen for males, and the nomen for females. A nobilis should always be called by his cognomen. A homo novus is normally called by his nomen unless the frequency of this particular nomen would make it unclear who you are talking about.
Where a person has more than one cognomen, you should normally use the first one. Calling someone by his agnomen, if he has one, is of course particularly complimentary. You should only call someone by his adoptive if you want to draw attention to his pre-adoption family and identity: this is not necessarily polite or impolite, but will depend on the context. Similarly calling someone by his matronymic cognomen will draw attention to his mother's identity and family.
Do not fall into the trap of calling someone routinely by his adoptive cognomen. This is often tempting, because it is an easy way of distinguishing between the adopted child and the adoptive father, but it is an un-Roman habit. To a Roman, an adopted child became, to all intents and purposes, the child of the adoptive parents, and one should normally ignore his adoptive cognomen when naming him.
The praenomen is essentially a private name, for use within the family. You should not call a Roman by just his praenomen unless he is your close relative or very, very close friend. Even spouses do not generally call each other by their praenomina alone - they generally use nomina or cognomina.
When you call someone by name, you have to use the vocative case and change the ending of the name to indicate that you are talking to the person, not about him. As a general rule, names ending in -us take an ending -e (e.g. Brutus -> Brute), though names ending in -ius turn to -i (e.g. Tullius -> Tulli). Names ending in -a and names with other endings do not change at all.
You may notice some people using vocative endings when they are talking about someone in the third person (e.g. "I was talking to Brute yesterday"). Don't be confused - you are right, they are wrong.
Addresses Other Than Names
Much more than in some modern Western societies, but similar to usage in modern Japan, for example, Romans addressed each other using labels other than names, or combine names with other terms. What follows is a very brief overview.
Dominus & Domina
Some modern Latin-speakers use "dominus" and "domina" as equivalents of English "Mr" and "Miss" or "Mrs". This is strongly discouraged. "Dominus" means "lord" or "master", and addressing someone in this way is very servile and grovelling.
An exception is that lovers sometimes call each other "dominus" and "domina", though usually only in the bedroom.
Though Romans do not generally go in for titles in a big way, it is not uncommon to call a Consul by the title "Consul", for example, especially when speaking in a political context or discussing business relevant to the office. Likewise one may call one's patron by the title "patronus". But titles are not by any means compulsory, and there is nothing at all rude in calling a magistrate straightforwardly by his name.
As well as calling each other by name, relatives commonly talk to or about each other by reference to their relationship, e.g. pater (father), soror (sister), patruus (uncle), &c. These terms are often combined with terms of endearment (see below). As noted above, close relatives might call each other by their praenomina.
Spouses and Lovers
As was mentioned above, spouses and lovers generally call each other by cognomen rather than praenomen. Occasionally they called each other vir (husband) and uxor (wife), but more commonly they used terms of endearment (see below).
Friends and Acquaintances
Most of the time people who know each other but are not especially close call each other by name, sometimes with "mi" (see below). Sometimes they will use brief descriptions, e.g. iuvenis (young man), amicus (friend), senex (old man). Depending on the relationship between the people concerned, they may use terms of endearment or even insults.
There is no direct Roman equivalent of "sir" or "madam". If you meet someone whose name you don't know, it is normal and not at all rude to say something like "petasate" ("you with the hat") or "senex" ("old man") or "viator" ("traveller"). Very often one might say "quiquis es" ("whoever you are").
Generally, though, unless you are merely asking the time of day, the best tactic is to try to find out the person's name by saying something like "adulescens, dic mihi nomen tuum, quaeso" ("young man, please tell me your name") or "o qui vocaris?" ("O how are you called?").
Terms of Endearment and Esteem
Romans have always been very inventive with terms of endearment. One very common one is "carissimus", often combined with a name, e.g. "salve Brute carissime" ("hello my dear Brutus"), "salve soror carissima" ("hello dear sister"). Others include "dulcis" ("sweet"), "inclitus" ("famous"), "magnus" ("great"), "optimus" ("excellent"), "fortissimus" ("very strong"). This should be enough to give you the general idea.
"Mi" and "O"
"Mi" (masculine) and "mea" (feminine) mean "my". They are very commonly attached to names or other terms of endearment in conversations between friends or well-meaning acquaintances, e.g. "salve mi frater" ("hello my brother"), "salve mea Cornelia" ("hello my Cornelia"). It is especially common in letters, not so much in oral conversation. 
"O" is also not uncommon. It has the general effect of making an address to someone more emotional, emphatic, or poetic. E.g. "o optime Brute" ("O excellent Brutus").
Personal Names in the Roman World